The document discusses functions and function components in C++. It introduces key concepts such as: - Functions allow programmers to divide programs into modular and reusable pieces. - Functions are defined once and can be called multiple times from different parts of a program. They take in parameters and return values. - The standard library provides many commonly used functions for tasks like math operations. - Functions can be used to encapsulate and reuse code through prototypes and definitions. - Enumerations allow defining a set of integer constants with unique names for use as variable types. - Storage classes like static and auto determine where variables are stored in memory and their scope within a program.

1. Functions

2. 3 Introduction
• Divide and conquer
– Construct a program from smaller pieces or components
– Each piece more manageable than the original program

3. 3.2 Program Components in C++
• Programs written by
– combining new functions with “prepackaged” functions in
the C++ standard library.
– new classes with “prepackaged” classes.
• The standard library provides a rich collection of
functions.
• Functions are invoked by a function call
– A function call specifies the function name and provides
information (as arguments) that the called function needs
– Boss to worker analogy:
A boss (the calling function or caller) asks a worker (the called
function) to perform a task and return (i.e., report back) the
results when the task is done.

4. 3.2 Program Components in C++
• Function definitions
– Only written once
– These statements are hidden from other functions.
– Boss to worker analogy:
The boss does not know how the worker gets the job done; he
just wants it done

5. 3.3 Math Library Functions
• Math library functions
– Allow the programmer to perform common mathematical
calculations
– Are used by including the header file <cmath>
• Functions called by writing
functionName (argument)
• Example
cout << sqrt( 900.0 );
– Calls the sqrt (square root) function. The preceding
statement would print 30
– The sqrt function takes an argument of type double and
returns a result of type double, as do all functions in the
math library

6. 3.3 Math Library Functions
• Function arguments can be
– Constants
sqrt( 4 );
– Variables
sqrt( x );
– Expressions
sqrt( sqrt( x ) ) ;
sqrt( 3 - 6x );

7. 3.4 Functions
• Functions
– Allow the programmer to modularize a program
• Local variables
– Known only in the function in which they are defined
– All variables declared in function definitions are local
variables
• Parameters
– Local variables passed when the function is called that
provide the function with outside information

8. Functions
• Why write functions?
– modularity
– re-use
– maintenance / testing

9. 3.5 Function Definitions
• Create customized functions to
– Take in data
– Perform operations
– Return the result
• Format for function definition:
return-value-type function-name( parameter-list )
{
declarations and statements
}
• Example:
int square( int y)
{
return y * y;
}

10. 1 // Fig. 3.3: fig03_03.cpp
2 // Creating and using a programmer-defined function
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 int square( int ); // function prototype
9
10 int main()
11 {
12 for ( int x = 1; x <= 10; x++ )
13 cout << square( x ) << " ";
14
15 cout << endl;
16 return 0;
17 }
18
19 // Function definition
20 int square( int y )
21 {
22 return y * y;
23 }
1 4 9 16 25 36 49 64 81 100
Notice how parameters and return
value are declared.

11. 1 // Fig. 3.4: fig03_04.cpp
2 // Finding the maximum of three integers
3 #include <iostream>
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 int maximum( int, int, int ); // function prototype
10
11 int main()
12 {
13 int a, b, c;
14
15 cout << "Enter three integers: ";
16 cin >> a >> b >> c;
17
18 // a, b and c below are arguments to
19 // the maximum function call
20 cout << "Maximum is: " << maximum( a, b, c ) << endl;

12. 21
22 return 0;
23 }
24
25 // Function maximum definition
26 // x, y and z below are parameters to
27 // the maximum function definition
28 int maximum( int x, int y, int z )
29 {
30 int max = x;
31
32 if ( y > max )
33 max = y;
34
35 if ( z > max )
36 max = z;
37
38 return max;
39 }
Enter three integers: 22 85 17
Maximum is: 85
Enter three integers: 92 35 14
Maximum is: 92
Enter three integers: 45 19 98
Maximum is: 98

13. 3.6 Function Prototypes
• Function prototype
– Function name
– Parameters
• Information the function takes in
• C++ is “strongly typed” – error to pass a parameter of the wrong type
– Return type
• Type of information the function passes back to caller (default int)
• void signifies the function returns nothing
– Only needed if function definition comes after the function
call in the program
• Example:
int maximum( int, int, int );
– Takes in 3 ints
– Returns an int

14. 3.7 Header Files
• Header files
– Contain function prototypes for library functions
– <cstdlib> , <cmath>, etc.
– Load with #include <filename>
• Example:
#include <cmath>
• Custom header files
– Defined by the programmer
– Save as filename.h
– Loaded into program using
#include "filename.h"

15. 3.8 Random Number Generation
• rand function
i = rand();
– Load <cstdlib>
– Generates a pseudorandom number between 0 and RAND_MAX
(usually 32767)
• A pseudorandom number is a preset sequence of "random" numbers
• The same sequence is generated upon every program execution
• srand function
– Jumps to a seeded location in a "random" sequence
srand( seed );
srand( time( 0 ) ); //must include <ctime>
– time( 0 )
• The time at which the program was compiled
– Changes the seed every time the program is compiled, thereby
allowing rand to generate random numbers

16. 3.8 Random Number Generation
• Scaling
– Reduces random number to a certain range
– Modulus ( % ) operator
• Reduces number between 0 and RAND_MAX to a number
between 0 and the scaling factor
– Example
i = rand() % 6 + 1;
• Generates a number between 1 and 6

17. 1 // Fig. 3.7: fig03_07.cpp
2 // Shifted, scaled integers produced by 1 + rand() % 6
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 #include <iomanip>
9
10 using std::setw;
11
12 #include <cstdlib>
13
14 int main()
15 {
16 for ( int i = 1; i <= 20; i++ ) {
17 cout << setw( 10 ) << ( 1 + rand() % 6 );
18
19 if ( i % 5 == 0 )
20 cout << endl;
21 }
22
23 return 0;
24 }
Notice rand() % 6 . This returns a number
between 0 and 5 (scaling). Add 1 to get a
number between 1 and 6.
Executing the program again gives the
same "random" dice rolls.
5 5 3 5 5
2 4 2 5 5
5 3 2 2 1
5 1 4 6 4

18. 1 // Fig. 3.9: fig03_09.cpp
2 // Randomizing die-rolling program
3 #include <iostream>
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 #include <iomanip>
10
11 using std::setw;
12
13 #include <cstdlib>
14
15 int main()
16 {
17 unsigned seed;
18
19 cout << "Enter seed: ";
20 cin >> seed;
21 srand( seed );
22
23 for ( int i = 1; i <= 10; i++ ) {
24 cout << setw( 10 ) << 1 + rand() % 6;
25
26 if ( i % 5 == 0 )
27 cout << endl;
28 }
29
30 return 0;
31 }

19. Program Output
Enter seed: 67
1 6 5 1 4
5 6 3 1 2
Enter seed: 432
4 2 6 4 3
2 5 1 4 4
Enter seed: 67
1 6 5 1 4
5 6 3 1 2
Notice how the die rolls
change with the seed.

20. 3.9 Example: A Game of Chance and
Introducing enum
• Enumeration - set of integers with identifiers
enum typeName {constant1, constant2…};
– Constants start at 0 (default), incremented by 1
– Unique constant names
– Example:
enum Status {CONTINUE, WON, LOST};
• Create an enumeration variable of type typeName
– Variable is constant, its value may not be reassigned
Status enumVar; // create variable
enumVar = WON; // set equal to WON
enumVar = 1; // ERROR

21. Example: A Game of Chance and
Introducing enum(II)
• Enumeration constants can have values pre-set
enum Months { JAN = 1, FEB, MAR, APR, MAY,
JUN, JUL, AUG, SEP, OCT, NOV, DEC};
– Starts at 1, increments by 1
• Craps simulator rules
– Roll two dice
• 7 or 11 on first throw, player wins
• 2, 3, or 12 on first throw, player loses
• 4, 5, 6, 8, 9, 10
– value becomes player's "point"
– player must roll his point before rolling 7 to win

22. 1 // Fig. 3.10: fig03_10.cpp
2 // Craps
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 #include <cstdlib>
9
10 #include <ctime>
11
12 using std::time;
13
14 int rollDice( void ); // function prototype
15
16 int main()
17 {
18 enum Status { CONTINUE, WON, LOST };
19 int sum, myPoint;
20 Status gameStatus;
21
22 srand( time( 0 ) );
23 sum = rollDice(); // first roll of the dice
24
25 switch ( sum ) {
26 case 7:
27 case 11: // win on first roll
28 gameStatus = WON;
29 break;
30 case 2:
31 case 3:
32 case 12: // lose on first roll
33 gameStatus = LOST;
34 break;
Notice how the
enum is defined

23. 35 default: // remember point
36 gameStatus = CONTINUE;
37 myPoint = sum;
38 cout << "Point is " << myPoint << endl;
39 break; // optional
40 }
41
42 while ( gameStatus == CONTINUE ) { // keep rolling
43 sum = rollDice();
44
45 if ( sum == myPoint ) // win by making point
46 gameStatus = WON;
47 else
48 if ( sum == 7 ) // lose by rolling 7
49 gameStatus = LOST;
50 }
51
52 if ( gameStatus == WON )
53 cout << "Player wins" << endl;
54 else
55 cout << "Player loses" << endl;
56
57 return 0;
58 }
59

24. Player rolled 6 + 5 = 11
Player wins
Player rolled 6 + 5 = 11
Player wins
Player rolled 4 + 6 = 10
Point is 10
Player rolled 2 + 4 = 6
Player rolled 6 + 5 = 11
Player rolled 3 + 3 = 6
Player rolled 6 + 4 = 10
Player wins
Player rolled 1 + 3 = 4
Point is 4
Player rolled 1 + 4 = 5
Player rolled 5 + 4 = 9
Player rolled 4 + 6 = 10
Player rolled 6 + 3 = 9
Player rolled 1 + 2 = 3
Player rolled 5 + 2 = 7
Player loses
60 int rollDice( void )
61 {
62 int die1, die2, workSum;
63
64 die1 = 1 + rand() % 6;
65 die2 = 1 + rand() % 6;
66 workSum = die1 + die2;
67 cout << "Player rolled " << die1 << " + " << die2
68 << " = " << workSum << endl;
69
70 return workSum;
71 }

25. 3.10 Storage Classes
• Storage class specifiers
– Storage class
• Where object exists in memory
– Scope
• Where object is referenced in program
– Linkage
• Where an identifier is known
• Automatic storage
– Object created and destroyed within its block
– auto
• Default for local variables.
• Example:
auto float x, y;
– register
• Tries to put variables into high-speed registers
– Can only be used with local variables and parameters

26. Storage Classes
• Static storage
– Variables exist for entire program execution
– static
• Local variables defined in functions
• Keep value after function ends
• Only known in their own function
– Extern
• Default for global variables and functions.
• Known in any function

27. Scope Rules
• File scope
– Defined outside a function, known in all functions
– Examples include, global variables, function definitions and
functions prototypes
• Function scope
– Can only be referenced inside a function body
– Only labels (start:, case:, etc.)
• Block scope
– Declared inside a block. Begins at declaration, ends at }
– Variables, function parameters (local variables of function)
– Outer blocks “hidden” from inner blocks if same variable name
• Function prototype scope
– Identifiers in parameter list
– Names in function prototype optional, and can be used anywhere

28. 1. Function prototypes
1.1 Initialize global variable
1.2 Initialize local variable
1 // Fig. 3.12: fig03_12.cpp
2 // A scoping example
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 void a( void ); // function prototype
9 void b( void ); // function prototype
10 void c( void ); // function prototype
11
12 int x = 1; // global variable
13
14 int main()
15 {
16 int x = 5; // local variable to main
17
18 cout << "local x in outer scope of main is " << x << endl;
19
20 { // start new scope
21 int x = 7;
22
23 cout << "local x in inner scope of main is " << x << endl;
24 } // end new scope
25
26 cout << "local x in outer scope of main is " << x << endl;
27
28 a(); // a has automatic local x
29 b(); // b has static local x
30 c(); // c uses global x
31 a(); // a reinitializes automatic local x
32 b(); // static local x retains its previous value
33 c(); // global x also retains its value
34
x is different inside and outside
the block.
local x in outer scope of main is 5
local x in inner scope of main is 7
local x in outer scope of main is 5

29. 3.1 Define Functions
35 cout << "local x in main is " << x << endl;
36
37 return 0;
38 }
39
40 void a( void )
41 {
42 int x = 25; // initialized each time a is called
43
44 cout << endl << "local x in a is " << x
45 << " after entering a" << endl;
46 ++x;
47 cout << "local x in a is " << x
48 << " before exiting a" << endl;
49 }
50
51 void b( void )
52 {
53 static int x = 50; // Static initialization only
54 // first time b is called.
55 cout << endl << "local static x is " << x
56 << " on entering b" << endl;
57 ++x;
58 cout << "local static x is " << x
59 << " on exiting b" << endl;
60 }
61
62 void c( void )
63 {
64 cout << endl << "global x is " << x
65 << " on entering c" << endl;
66 x *= 10;
67 cout << "global x is " << x << " on exiting c" << endl;
68 }
Local automatic variables are
created and destroyed each
time a is called.
Local static variables are
not destroyed when the
function ends.
Global variables are always
accessible. Function c
references the global x.
local x in a is 25 after entering a
local x in a is 26 before exiting a
local static x is 50 on entering b
local static x is 51 on exiting b
global x is 1 on entering c
global x is 10 on exiting c

30. local x in outer scope of main is 5
local x in inner scope of main is 7
local x in outer scope of main is 5
local x in a is 25 after entering a
local x in a is 26 before exiting a
local static x is 50 on entering b
local static x is 51 on exiting b
global x is 1 on entering c
global x is 10 on exiting c
local x in a is 25 after entering a
local x in a is 26 before exiting a
local static x is 51 on entering b
local static x is 52 on exiting b
global x is 10 on entering c
global x is 100 on exiting c
local x in main is 5

31. References and Reference
Parameters
• Call by value
– Copy of data passed to function
– Changes to copy do not change original
– Used to prevent unwanted side effects
• Call by reference
– Function can directly access data
– Changes affect original
• Reference parameter alias for argument
– & is used to signify a reference
void change( int &variable )
{ variable += 3; }
– Adds 3 to the variable inputted
int y = &x.
– A change to y will now affect x as well

32. 1 // Fig. 3.20: fig03_20.cpp
2 // Comparing call-by-value and call-by-reference
3 // with references.
4 #include <iostream>
5
6 using std::cout;
7 using std::endl;
8
9 int squareByValue( int );
10 void squareByReference( int & );
11
12 int main()
13 {
14 int x = 2, z = 4;
15
16 cout << "x = " << x << " before squareByValuen"
17 << "Value returned by squareByValue: "
18 << squareByValue( x ) << endl
19 << "x = " << x << " after squareByValuen" << endl;
20
21 cout << "z = " << z << " before squareByReference" << endl;
22 squareByReference( z );
23 cout << "z = " << z << " after squareByReference" << endl;
24
25 return 0;
26 }
27
28 int squareByValue( int a )
29 {
30 return a *= a; // caller's argument not modified
31 }

33. x = 2 before squareByValue
Value returned by squareByValue: 4
x = 2 after squareByValue
z = 4 before squareByReference
z = 16 after squareByReference
32
33 void squareByReference( int &cRef )
34 {
35 cRef *= cRef; // caller's argument modified
36 }

34. 3.12 Recursion
• Recursive functions
– Are functions that calls themselves
– Can only solve a base case
– If not base case, the function breaks the problem into a
slightly smaller, slightly simpler, problem that resembles the
original problem and
• Launches a new copy of itself to work on the smaller problem,
slowly converging towards the base case
• Makes a call to itself inside the return statement
– Eventually the base case gets solved and then that value
works its way back up to solve the whole problem

35. Recursion
• Example: factorial
n! = n * ( n – 1 ) * ( n – 2 ) * … * 1
– Recursive relationship ( n! = n * ( n – 1 )! )
5! = 5 * 4!
4! = 4 * 3!…
– Base case (1! = 0! = 1)

36. The Fibonacci Series
• Fibonacci series: 0, 1, 1, 2, 3, 5, 8...
– Each number sum of two previous ones
– Example of a recursive formula:
fib(n) = fib(n-1) + fib(n-2)
• C++ code for fibonacci function
long fibonacci( long n )
{
if ( n == 0 || n == 1 ) // base case
return n;
else if ( n < 0 )
return –1;
else
return fibonacci( n - 1 ) + fibonacci( n – 2 );
}

37. The Fibonacci Series
• Diagram of Fibonnaci function
f( 3 )
f( 1 )
f( 2 )
f( 1 ) f( 0 ) return 1
return 1 return 0
return +
+
return

38. 1. Function prototype
1.1 Initialize variables
2. Input an integer
1 // Fig. 3.15: fig03_15.cpp
2 // Recursive fibonacci function
3 #include <iostream>
4
5 using std::cout;
6 using std::cin;
7 using std::endl;
8
9 unsigned long fibonacci( unsigned long );
10
11 int main()
12 {
13 unsigned long result, number;
14
15 cout << "Enter an integer: ";
16 cin >> number;
17 result = fibonacci( number );
18 cout << "Fibonacci(" << number << ") = " << result << endl;
19 return 0;
20 }
21
22 // Recursive definition of function fibonacci
23 unsigned long fibonacci( unsigned long n )
24 {
25 if ( n == 0 || n == 1 ) // base case
26 return n;
27 else // recursive case
28 return fibonacci( n - 1 ) + fibonacci( n - 2 );
29 }

39. Program Output
Enter an integer: 0
Fibonacci(0) = 0
Enter an integer: 1
Fibonacci(1) = 1
Enter an integer: 2
Fibonacci(2) = 1
Enter an integer: 3
Fibonacci(3) = 2
Enter an integer: 4
Fibonacci(4) = 3
Enter an integer: 5
Fibonacci(5) = 5
Enter an integer: 6
Fibonacci(6) = 8
Enter an integer: 10
Fibonacci(10) = 55
Enter an integer: 20
Fibonacci(20) = 6765
Enter an integer: 30
Fibonacci(30) = 832040
Enter an integer: 35
Fibonacci(35) = 9227465

40. 3.14 Recursion vs. Iteration
• Repetition
– Iteration: explicit loop
– Recursion: repeated function calls
• Termination
– Iteration: loop condition fails
– Recursion: base case recognized
• Both can have infinite loops
• Balance between performance (iteration) and good
software engineering (recursion)

41. Functions with Empty Parameter Lists
• Empty parameter lists
– Either writing void or leaving a parameter list empty
indicates that the function takes no arguments
void print();
or
void print( void );
– Function print takes no arguments and returns no value

42. 1 // Fig. 3.18: fig03_18.cpp
2 // Functions that take no arguments
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 void function1();
9 void function2( void );
10
11 int main()
12 {
13 function1();
14 function2();
15
16 return 0;
17 }
18
19 void function1()
20 {
21 cout << "function1 takes no arguments" << endl;
22 }
23
24 void function2( void )
25 {
26 cout << "function2 also takes no arguments" << endl;
27 }
function1 takes no arguments
function2 also takes no arguments

43. Inline Functions
• inline functions
– Reduce function-call overhead
– Asks the compiler to copy code into program instead of using a
function call
– Compiler can ignore inline
– Should be used with small, often-used functions
• Example:
inline double cube( const double s )
{ return s * s * s; }

44. 3.18 Default Arguments
• If function parameter omitted, gets default value
– Can be constants, global variables, or function calls
– If not enough parameters specified, rightmost go to their
defaults
• Set defaults in function prototype
int defaultFunction( int x = 1,
int y = 2, int z = 3 );

45. 1 // Fig. 3.23: fig03_23.cpp
2 // Using default arguments
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 int boxVolume( int length = 1, int width = 1, int height = 1 );
9
10 int main()
11 {
12 cout << "The default box volume is: " << boxVolume()
13 << "nnThe volume of a box with length 10,n"
14 << "width 1 and height 1 is: " << boxVolume( 10 )
15 << "nnThe volume of a box with length 10,n"
16 << "width 5 and height 1 is: " << boxVolume( 10, 5 )
17 << "nnThe volume of a box with length 10,n"
18 << "width 5 and height 2 is: " << boxVolume( 10, 5, 2 )
19 << endl;
20
21 return 0;
22 }
23
24 // Calculate the volume of a box
25 int boxVolume( int length, int width, int height )
26 {
27 return length * width * height;
28 }

46. Program Output
The default box volume is: 1
The volume of a box with length 10,
width 1 and height 1 is: 10
The volume of a box with length 10,
width 5 and height 1 is: 50
The volume of a box with length 10,
width 5 and height 2 is: 100

47. 3.19 Unary Scope Resolution Operator
• Unary scope resolution operator (::)
– Access global variables if a local variable has same name
– not needed if names are different
– instead of variable use ::variable

48. 1 // Fig. 3.24: fig03_24.cpp
2 // Using the unary scope resolution operator
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 #include <iomanip>
9
10 using std::setprecision;
11
12 const double PI = 3.14159265358979;
13
14 int main()
15 {
16 const float PI = static_cast< float >( ::PI );
17
18 cout << setprecision( 20 )
19 << " Local float value of PI = " << PI
20 << "nGlobal double value of PI = " << ::PI << endl;
21
22 return 0;
23 }
Local float value of PI = 3.141592741012573242
Global double value of PI = 3.141592653589790007

49. 3.20 Function Overloading
• Function overloading
– Having functions with same name and different parameters
– Should perform similar tasks ( i.e., a function to square
ints, and function to square floats).
int square( int x) {return x * x;}
float square(float x) { return x * x; }
– Program chooses function by signature
• signature determined by function name and parameter types
– Can have the same return types

50. 1 // Fig. 3.25: fig03_25.cpp
2 // Using overloaded functions
3 #include <iostream>
4
5 using std::cout;
6 using std::endl;
7
8 int square( int x ) { return x * x; }
9
10 double square( double y ) { return y * y; }
11
12 int main()
13 {
14 cout << "The square of integer 7 is " << square( 7 )
15 << "nThe square of double 7.5 is " << square( 7.5 )
16 << endl;
17
18 return 0;
19 }
The square of integer 7 is 49
The square of double 7.5 is 56.25